Embibe Experts Solutions for Chapter: Properties of Triangle, Exercise 1: Exercise 1

In a triangle $ABC,$ points $D$ and $E$ are taken on side $BC$ such that $BD=DE=EC.$ If angle $ADE=$ angle $AED=\theta ,$ then-

In a triangle $ABC,\frac{a}{b}=2+\sqrt{3},\angle C=60°$, then in the triangle

In a $\Delta ABC,a\cos B+b\cos C+c\cos A=\frac{a+b+c}{2}$ then

In a triangle $ABC,$ right angled at $B,$ then

With usual notations, in a $△ABC$ the value of $\prod \left(r_1-r\right)$ can be simplified as-

In a triangle $ABC$ -

$D, E. F$ are the foot of thee perpendiculars from vertices $A, B, C$ to sides $BC, CA, AB$ respectively, and $H$ is the orthocentre of acute angled triangle $ABC$, where $a,b,c$ are the sides of triangle $ABC$, then

If $a\cos B \cos C+b\cos C\cos A+c\cos A \cos B=\frac{\lambda \Delta }{2R}$, then find the value of $\lambda$.